RMO 2023 K1

Given a triangle $ABC$ with $\angle ACB = 120^{\circ}.$ A point $L$ is marked in the side $AB$ such that $CL$ bisects $\angle ACB.$ Points $N$ and $K$ are chosen in the sides $AC$ and $BC$ such that $CK+CN=CL.$ Prove that the triangle $KLN$ is equilateral.